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Thread: Quotient Rule

  1. June 6th 2008, 10:48 AM #1
    omkara
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    Quotient Rule

    (A)(i) Use the Quotient Rule to differentiate the function
    h(x) = 1 + In x (x > 0)
    xxxxxxxxx

    Please can somone help me before I pull my hair.
    Thank you in advance
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  2. June 6th 2008, 10:51 AM #2
    Mathstud28
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    Quote Originally Posted by omkara View Post
    (A)(i) Use the Quotient Rule to differentiate the function
    h(x) = 1 + In x (x > 0)
    xxxxxxxxx

    Please can somone help me before I pull my hair.
    Thank you in advance
    I am unaware of what In(x) is?

    But I will assume the problem reads

    \frac{1+\color{red}{\ln(x)}}{x}

    In which case the quotient rule gives

    \frac{x\bigg(\frac{1}{x}\bigg)-(1+\ln(x))(1)}{x^2}

    Is that right?
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  3. June 6th 2008, 10:54 AM #3
    janvdl
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    Quote Originally Posted by omkara View Post
    (A)(i) Use the Quotient Rule to differentiate the function
    h(x) = 1 + In x (x > 0)
    xxxxxxxxx

    Please can somone help me before I pull my hair.
    Thank you in advance
    h(x) = \frac{1 + ln x}{x}

    h'(x) = \frac{(1 + ln x)'(x) - (x)'(1 + ln x)}{x^2}

    h'(x) = \frac{(\frac{1}{x})(x) - (1)(1 + ln x)}{x^2}

    h'(x) = \frac{(1 - (1 + ln x)}{x^2}

    h'(x) = \frac{(-ln x)}{x^2}
    Last edited by janvdl; June 6th 2008 at 10:57 AM. Reason: I seem to be on the slow side tonight... Everyone beats me to questions :D
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